Phase transition of fractional Chern insulators: QED3 and beyond

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Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED3-Chern-Simons theory. At these critical points, Nf flavors of Dirac fermions interact through an emergent U(1) gauge theory at Chern-Simons level K, and remarkably, the entire family (with any Nf or K) can be realized at special values of the external magnetic field. I will talk about the physical properties and microscopic realization of those critical points. We propose experiments on Chern insulators that could resolve open questions in the study of 2+1 dimensional conformal field theories and test recent duality inspired conjectures.